'Cubist Cuts' printed from http://nrich.maths.org/

A $3 \times 3 \times 3$ cube may be reduced to unit cubes ($1
\times1 \times1$ cubes) in six saw cuts if you go straight at
it.

If after every cut you can rearrange the pieces before cutting
straight through, can you do it in fewer? Answer the same question
with a $4 \times 4 \times 4$ cube:

What about a cube of any size (an $n \times n \times n$
cube)?

This problem is taken from "Sums for Smart Kids" by Laurie
Buxton, published by BEAM Education. To obtain a copy call the BEAM
orderline on 020 7684 3330 quoting product code SMAR. (Price:
£13.50 plus handling and delivery.)